Re: cube root of a given number

On 22 Jul, 23:47, arithmonic <djes...@xxxxxxxxx> wrote:
On 22 jul, 07:29, "sttscitr...@xxxxxxxxx" <sttscitr...@xxxxxxxxx>
wrote:

On 22 Jul, 04:28, arithmonic <djes...@xxxxxxxxx> wrote:

On 21 jul, 17:39, "sttscitr...@xxxxxxxxx" <sttscitr...@xxxxxxxxx>
wrote:

On 21 Jul, 21:38, arithmonic <djes...@xxxxxxxxx> wrote:

On 16 jul, 04:39, "sttscitr...@xxxxxxxxx" <sttscitr...@xxxxxxxxx>

1.- I challenge you to show such Eshbach's method in this thread,
because both of you are trying to state that my methods --based on the
Rational Mean-- are the same as the one you read in Eshbach's
work ("Handbook of Engineering Fundamentals).

I'm sure the poster knows what he read.

Why are you so sure? Are you his friend?
I am sure that the poster called Grover Hughes does not know a single
bit of all what he was talking about, tha's why I challenged him and
be sure the method he mentioned is by far similar to the methods shown
in my web pages. The sci.math audience is also waiting and observing
the results of my challenges to both of you.

Now to the very specific point on ROOTS-SOLVING METHODS:



2.- I challenged you in this posting to show to the sci.math audience
a very simple numerical example on your alleged GENERAL Hurwitz's
ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2.

There are 5 fifth roots of 2. Which one do you want ?
Are you saying you can find complex roots too ?

Finding the real root of x^5-2 =0 is simple.
s(x,y) is the sign of binary quntic x^5-2y^5

The root must lie between (0,1) = 0 and (1,0) = "inf"
calculate s(0,1) and s(1,0). Form the mediant (1,1)
At any stage in the process s(xn,yn) will be 1 or -1.
if s(xn,yn) = un The new new mediant is formed with
(xk,yk) where k is the largest index <n such that un*uk = -1

0 1 -1
1 0 1
1 1 -1
2 1 1
3 2 1
4 3 1
5 4 1
6 5 1
7 6 1
8 7 -1
15 13 1
23 20 1
31 27 -1
54 47 1
85 74 -1
139 121 1
224 195 1
309 269 1
394 343 -1
703 612 -1
1012 881 -1
1321 1150 -1
1630 1419 -1
1939 1688 -1
2248 1957 -1
2557 2226 -1
2866 2495 -1
3175 2764 -1
3484 3033 -1
3793 3302 -1
4102 3571 -1
4411 3840 -1
4720 4109 -1
5029 4378 -1
5338 4647 -1
5647 4916 -1
5956 5185 -1
6265 5454 -1
6574 5723 -1
6883 5992 -1
7192 6261 -1
7501 6530 -1
7810 6799 -1
8119 7068 1
15929 13867 -1
24048 20935 -1
32167 28003 -1
40286 35071 -1
48405 42139 1
88691 77210 1
128977 112281 1
169263 147352 -1
298240 259633 -1

Can you solve x^3 -2x^2 -x+1 =0 ?

Notice that I am challenging you and your friend Grover Hughes with two very simple inquires.

I don't know why you think Grover Hughes is a friend of mine.

You used to claim that you could find the best simultaneous
approximations to cubrt(2), cubrt(4).
As you methods are so revolutionary, I would have thought
this would have been possible too.

In fact, you can use your methods for simultaneous approximation of
cubrt(2), cubrt(4), but it would be
sheer luck if a best approximation was found.
Shall I give you a hint ?

Do you understand the diffference between fast convergence and best
rational approximation ?

One step at the time, please.

Let us focus on the main point of this thread: The extremely simple
high-order arithmetical methods shown in my webpages, and your
allegued Hurtwitz's Root-Solving Method as being the same thing that
my methods, in such a way, that when talking about them you stated: "I
don't think the claim that these methods are in any way new stands up
to scrutiny."

Only after clarifying this point to the sci.math audience I will
procede to answer all the other
remarks you have made in this posting.

But... Please, If you don't mind, I want to ask you just two more
questions specifically related to this table you have shown on the
fifth root and your remark about the methods shown in my webpages: "I
don't think the claim that these methods are in any way new stands up
to scrutiny."

ARE YOU JUST PLAYING A JOKE OR WHAT?
HAVE YOU EVER READ A BOOK ON THE HISTORY OF MATHEMATICS?

What I find strabge is that you claim to have invented
a new method of root solving and yet seem to be incapable
of applying it to any problem I pose.

Can you solve x^3 -2x^2 -x+1 =0 ?
Why is it that I can apply your method to simultaneously
approximate cubrt(2), cubrt(4) but you can't. ?


.

Relevant Pages

  • Re: cube root of a given number
    ... ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2. ... sheer luck if a best approximation was found. ... to scrutiny." ... remarks you have made in this posting. ...
    (sci.math)
  • Re: time complexity
    ... Finding the real value is not exactly a simple mathematical exercise. ... Zeroin returns an estimate for the root with accuracy ... b - the last and the best approximation to the root ... double tol) ...
    (comp.lang.c)
  • Re: Game Tree Programming Idea: Selectivity via modified alpha-beta pruning
    ... returns a score of 1.00 up to the root. ... idea will be good for alpha beta too. ... One can quite easily conclude that if you do this approximation (by ... root is no more than K * delta. ...
    (rec.games.chess.computer)
  • Re: cube root of a given number
    ... ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2. ... Form the mediant ... you can use your methods for simultaneous approximation of ... sheer luck if a best approximation was found. ...
    (sci.math)
  • Re: Simple and good approximations to the additive partition function
    ... your remarks are very enlightening! ... It's interesting to see that even the first term in Rademacher's ... formula provides such an impressive approximation. ... >> to the additive partition function p. ...
    (sci.math)
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